finding the phase shift

Question

let y = √20sin(4piex+7e^-1)

what is the amplitude?

what is the period?

what is the phase shift? 

Answer 1

Amp A = √20

Period T = 1/2 (solving 4piT = 2pi for T.)

Phase shift φ = -7/(4pi e) (solving 4piφ+7/e = 0 for φ.)

Answer 2

Let's compare your equation to that of a general sinusoidal oscillation:

 

y = A sin ((2*Pi/T) x - φ),

 

where A is the amplitude, T the period, and φ the phase shift. You have

 

y = √20 sin ((4*Pi) x + 7e^-1),

 

therefore the amplitude is A=√20, the period we get from

 

2*Pi/T = 4*Pi, which gives us T=1/2,

 

and the phase shift is φ=-7e^-1.

 

With this information you should be able to sketch the graph of the oscillation.